Mathematical Programming

Environmental pollution and rapid depletion are among the chief concerns about fossil fuels such as oil, gas, and coal. Renewable energy sources do not suffer from such limitations and are considered the best choice to replace fossil fuels. The present study develops a mathematical model for optimal allocation of regional renewable energy to meet a country-wide demand and its other essential aspects. The ultimate purpose is to minimize the total cost by planning, including power plant construction and maintenance costs and transmission costs. Minimum-cost flow equations are embedded in the model to determine how regions can supply energy to other regions or rely on them to fulfill annual demand. In order to verify the applicability of the model, it is applied to a real-world case study of Iran to determine the optimal renewable energy generation-transmission decisions for the next decade. Results indicate that the hydroelectric and solar power plants should generate the majority of the generated renewable electricity within the country, according to the optimal solution. Moreover, regarding the significant population growth and waste generation in the country’s large cities, biomass power plants can have the opportunity to satisfy a remarkable portion of electricity demand.

INTRODUCTION: In times of crisis, the timely transfer of the injured to medical facilities is one of the most important stages of relief and one of the most widely used methods to achieve the transfer point designing goal. The transfer point in literature is a place to collect and transfer the optimal demand for a particular service. For example, in times of natural disasters such as earthquakes, the injured (customers) are transferred by ambulance to the transfer points and then by helicopter to the hospital (facility). METHODS: In this study, two single-objective and double-objective complex integer number programming models were presented for the problem of locating transfer points and optimal allocation to facilities, taking into account the limitations in facility capacity and transfer points as well as assuming two types of normal and bad injuries. FINDINGS: In the single-objective model, the reduction in the time of sending the injured in the relief chain, and in the double objective model, in addition to the previous goal, the reduction of the fine for not sending the injured were examined. It is only possible to transfer each injured person to the hospital using the transfer points, and the treatment of the normally injured individuals is performed at the transfer points. The models were solved with two approaches, mild and severe. In order to show the efficiency of the proposed models, a case study was conducted in districts 10, 11, and 17 of Tehran metropolis, Iran. CONCLUSION: Setting up transfer points has a great impact on speeding up the process of providing services to the injured. Additionally, given the disproportionality of the number of injured with the capacity of hospitals in severe crises, it is necessary to anticipate transfer points to manage relief and respond to all injured.